Milan Holický

Design characteristics of structural steels based on statistical analysis of metallurgical products

Abstract The results of experimental research of material and geometrical characteristics of Czech steel are given in the present paper. The yield strength, tensile strength and ductility were evaluated statistically. For hot-rolled steel IPE profiles, the geometrical characteristics of cross-section dimensions were evaluated statistically too. It has been proved that both material and geometrical characteristics of plates and hot-rolled IPE profiles are satisfactory. The problems are discussed also in connection with application of stochastic computations. For this purpose, correlation coefficients among the quantities measured were also investigated.

Fuzzy probabilistic optimisation of building performance

Fundamental performance criteria between action effects and relevant performance requirements for serviceability, safety, comfort and functionality are analyzed, assuming randomness of the effect action and both randomness and fuzziness of performance requirements. Randomness due to natural variability of basic variables is handled by commonly used probability theory methods, fuzziness due to vague or imprecise definitions of performance requirements is described by basic tools of the recently developed theory of fuzzy sets. Both types of uncertainties are combined in newly defined fuzzy probabilistic measures of building performance, damage function and fuzzy probability of performance failure, which are then analysed and applied similarly as conventional probabilistic quantities. An illustrative example of optimization of vibration constraints for building structures due to occupancy comfort indicates that commonly considered limiting values for acceleration may be uneconomical. However, theoretical models used to describe fuzzy probabilistic properties of performance requirements need to be reexamined using adequate experimental data.

Optimisation of the target reliability for temporary structures

The target reliability levels recommended in various national and international documents vary within a broad range, while the reference to the failure consequences and design working life is made only very vaguely. In some cases, the target reliability indexes are indicated for one or two reference periods (for 1 year and 50 years); however, no explicit link to the design working life, which is important particularly for temporary structures, is usually provided. This contribution attempts to clarify the relationship between the optimum target reliability of temporary structures, failure consequences, the design working life and the discount rate. The theoretical study based on probabilistic optimisation is supplemented by recommendations useful for code-makers and required by practicing engineers. It appears that the optimum reliability indexes depend primarily on the ratio of the cost of structural failure to the cost per unit of the structural parameter and less significantly on the design working life and the discount rate.

Testing of Statistical Hypotheses

The testing of statistical hypotheses is one of the essential topics of mathematical statistics, and is often used in engineering and scientific applications. In general, a given hypothesis about a population based on limited sample data is verified specifying a certain high probability (0.95) that the hypothesis is accepted. The complementary small probability (0.05), called significance level, is the probability that the hypothesis will be rejected, even though it is correct (Type I error). Another error may occur when the hypothesis is accepted, although incorrect (Type II error). Operational techniques are provided for testing the deviation of a sample mean from the population mean, testing the deviation of a sample variance from the population variance, testing the difference between two sample means, and testing difference between two sample variances. Two additional frequently applied tests are included: tests of good fit of a given theoretical model, and the testing of outliers in a sample.

Assessment of Flooding Risk to Cultural Heritage in Historic Sites

Fluvial flooding in August 2002 affected a number of structures in the Czech Republic. Considerable damage was observed particularly in the historic city of Prague. Extensive investigations indicated that main observed causes of damage could be classified into geotechnical aspects, inadequate structural properties, and insufficient communication. After the flooding responsible authorities have considered permanent and temporary protective measures to reduce adverse consequences of flooding in the future. Decisions concerning expensive measures should be preferably based on risk optimization, taking into account potential societal and economic consequences and losses of cultural heritage values. General framework of the risk assessment is thus proposed considering specific issues of cultural heritage. Such an assessment needs a theoretical model suitable for predicting flows and extents of future floods. For that reason, the authors statistically analyzed hydrologic data for annual maximum flows of the Vltava River in Prague dating back to 1827. Pearson III and lognormal distributions seem to be suitable models for a considered sample. Estimations of extreme flows, needed for assessment of flooding risk to endangered sites and decisions on protective measures, are provided for different return periods.

Target Reliability Levels in Present Standards

Abstract The target reliability levels recommended in national and international documents vary within a broad range, while the reference to relevant costs and failure consequences is mentioned only very vaguely. In some documents the target reliability index is indicated for one or two reference periods (1 year, 50 years or life-time) without providing appropriate links to the design working life. This contribution attempts to clarify the relationship between the target reliability levels, costs of safety measures, failure consequences, reference periods and the design working life

MODEL UNCERTAINTY FOR SHEAR RESISTANCE OF REINFORCED CONCRETE BEAMS WITH SHEAR REINFORCEMENT ACCORDING TO EN 1992-1-1

Abstract The submitted contribution is focused on the model uncertainty related to shear resistance of reinforced concrete beams with special shear reinforcement considering available test results. Variation of the model uncertainty with basic variables is analysed and significant variables are identified for the section-oriented formula provided in EN 1992-1-1. Proposed probabilistic description of the model uncertainty consists of the lognormal distribution having the coefficient of variation of about 0.25 and the mean significantly varying with the strength of shear reinforcement

Reliability and Risk Acceptance Criteria for Civil Engineering Structures

Abstract The specification of risk and reliability acceptance criteria is a key issue of reliability verifications of new and existing structures. Current target reliability levels in standards appear to have considerable scatter. Critical review of risk acceptance approaches to societal, economic and environmental risk indicates that an optimal design strategy is mostly dominated by economic aspects while human safety aspects need to be verified only in special cases. It is recommended to specify the target levels considering economic optimisation and the marginal life-saving costs principle, as both these approaches take into account the failure consequences and costs of safety measures.

Strength assessment of historic brick masonry

AbstractThe identification of residual service life of a structure is an exceptionally demanding task in the case of reconstructed or newly modernised buildings. The identification of residual service life requires the study and knowledge of the mutual interaction of a building with its external environment, in particular, the time variable effects and impacts which lead to degradation processes and phenomena affecting and, in the absolute majority of cases, degrading the physical, mechanical and other properties of materials and structures. The article presents the results of in-situ and laboratory research of strength parameters of masonry from the start of the 20th century applying destructive and non-destructive tests. Besides, a probabilistic model and a procedure for the determination of masonry strength are described. It appears that the probabilistic approach leads to a design value by ca 5% higher than the deterministic approach.

Functions of Random Variables

Functions of random variables defining resulting random variables as functions of several input random variables regularly enter many engineering and scientific applications. The elementary functions of a single continuous variable and two or more independent variables, reviewed in Appendix 4, are supplemented by functions several random variables. A special function of a single random variable is the extreme value of samples taken from a population described by various types of so-called extreme value distributions. These distributions play a substantial role in a number of practical applications. Another important function of a random variable is the updating of its probability distribution when newly obtained information is taken into account. This procedure is developed as an extension of Bayes´ theorem. Finally, the distribution of a sum of several random variables is discussed in conjunction with the central limit theorem.